Suppose you have a carracosta with a jolly nature and max speed ivs, and it uses shell smash. What is the fastest Pokemon it could outspeed? I know it can beat an unscarfed tangrowth after a boost, but not swoobat, which sits at 114 base speed. In short, what base speed does it beat after a shell smash boost without resorting to aqua jet? I'm guessing it's roughly base 80-85, but i'd like a second opinion.

Base stats are deceptive because you need to calculate things like EVs, IVs and natures as well. It's not practical to EV train a Tangrowth in speed since it's so slow, so it's better to invest in defences instead. Carracosta will most likely outspeed Tangrowth.

For Swoobat, speed is commonly EV trained, so it would depend on both Pokemon's IVs as to whether Carrcosta can outspeed it.

I know this is already answered Multiple times, but the Fastest Pokemon you can outspeed would be Serperioir
(I know this is not the correct way to spell, I will change)
Becuase Serperior has a base speed of 113 you would be able to out speed it.

Alright, a max speed, Jolly Carracosta at +2 speed has 358 Speed, and dissappointingly, Timid Swoobat has 359 speed, meaning that if Swwobat has Carracosta outsped by 1 speed, which is a big bummer. At +2 with max speed, Carracosta will be oustpeeding Timid/Jolly non-Scarfed Base 113's and non-scarfed 129's that do not have a speed increasing nature. Note that basically most scarfers will outspeed you. Try giving Carroacosta a Salac Berry, which will raise his speed by one stage when he drops below 25% HP, which will work well with Sturdy, and put his speed up to 537 after a Shell Smash and Salac boost, at which point you will mostly be fearing priority.